Mathematics
If two diameters of a circle intersect each other at right angles, then the quadrilateral formed by joining their end points is a :
rhombus
square
rectangle
parallelogram
Answer
Let the two diameters AB and CD intersect at the centre O at right angles.
The quadrilateral formed by joining the end points in order is ACBD.
In ΔAOC, ΔCOB, ΔBOD, ΔDOA , we have two sides which are radii and an included angles as 90°. Therefore, by SAS theorem, all triangles are congruent.
Thus, all four sides are equal AC = CB = BD = DA.
Each interior angle of the quadrilateral (e.g., ∠ACB) is an angle inscribed in a semicircle. Thus, each interior angle equals to 90°.
A quadrilateral with all sides equal, and all angles equal to 90° is a square.
Hence, option 2 is the correct option.
Related Questions
The angle formed in a major segment of a circle is :
an acute angle
an obtuse angle
a right angle
either an acute or an obtuse angle
An equilateral triangle ABC is inscribed in a circle with centre O. The measure of ∠BOC is :
120°
60°
90°
30°
In the given figure, O is the centre of the circle such that ∠AOC = 130°, then ∠ABC is equal to :
65°
90°
105°
115°
A chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is :
60°
90°
120°
150°